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Abstract

Nanoindentation tests were performed on nanostructured transparent magnesium aluminate
(MgAl2O4) ceramics to determine their mechanical properties. These tests were carried out
on samples at different applied loads ranging from 300 to 9,000 μN. The elastic recovery
for nanostructured transparent MgAl2O4 ceramics at different applied loads was derived from the force-depth data. The results
reveal a remarkable enhancement in plastic deformation as the applied load increases
from 300 to 9,000 μN. After the nanoindetation tests, scanning probe microscope images
show no cracking in nanostructured transparent MgAl2O4 ceramics, which confirms the absence of any cracks and fractures around the indentation.
Interestingly, the flow of the material along the edges of indent impressions is clearly
presented, which is attributed to the dislocation introduced. High-resolution transmission
electron microscopy observation indicates the presence of dislocations along the grain
boundary, suggesting that the generation and interaction of dislocations play an important
role in the plastic deformation of nanostructured transparent ceramics. Finally, the
experimentally measured hardness and Young’s modulus, as derived from the load–displacement
data, are as high as 31.7 and 314 GPa, respectively.

Keywords:

Background

Magnesium aluminate (MgAl2O4) spinel transparent ceramic has been considered as an important optical material
due to its good mechanical properties and excellent transparency from visible light
to infrared wavelength range [1]. However, it is well known that their intrinsic fracture toughness (premature failure
due to brittle fracture) [2-4] limits their wide applications in severe environments. Therefore, there has been
great interest in the investigation of ceramic materials with improved toughness [5-8]. In particular, it has been believed that nanostructured ceramics may have greatly
improved mechanical properties when compared with their conventional large-grained
counterparts [9].

In our previous work [10,11], we employed a novel technique to study the fabrication of nanostructured transparent
ceramics. Moreover, we analyzed the transparency mechanism in these ceramics. Nanoindentation
is a powerful technique widely employed to determine the mechanical properties of
nanostructured materials [12,13]. However, during the past decades, nanoindentation test has been widely utilized
to measure the mechanical properties of numerous materials including polycrystalline
ceramics [14-16] rather than those of nanostructured transparent ceramics. In this paper, we use the
nanoindentation technique to probe the mechanical properties of nanostructured transparent
MgAl2O4 ceramics.

Methods

High-purity nanostructured transparent MgAl2O4 ceramics with a grain size of approximately 40 nm, fabricated by high pressure-temperature
sintering [10], were selected as the test material for the present study. The mechanical properties
of ceramic samples were characterized using a nanoindentation technique (Hysitron
Inc., Minneapolis, MN, USA). Nanoindentation experiments were carried out on the samples
with a diamond Berkovich (three-sided pyramid) indenter. In all loading-unloading
cycles, loading and unloading lasted 2 s, respectively, and with a pause at a maximum
load (Pmax) of 5 s. More than 20 indentations were performed at each load. The employed load
ranges from 300 to 9,000 μN. Hardness (H) and Young’s modulus (Er) were calculated based on the model of Oliver and Pharr approach [17]. The nanostructure of the samples was investigated by means of high-resolution transmission
electron microscopy (HRTEM). The residual nanoindentation imprints were observed using
a scanning probe microsope (SPM).

Results and discussion

Figure 1 shows a typical load-depth curve obtained through nanoindentation in the present
study. The inset shows the difference between the total indentation depth at a maximum
indented load (hmax) and depth of residual impression upon unloading (hf), i.e., the elasticity recovery hmax − hf. Following the nanoindentation load-depth data, the H and Er were determined [17]; these quantities can be derived using the following relations:

(1)

(2)

(3)

(4)

(5)

where S is the elastic constant stiffness defined as the slope of the upper portion of the
unloading curve, as shown in Figure 1, hc is the contact depth, ϵ is the strain (0.75 for the Berkovich indenter), Pmax is the maximum applied load, A is the projected contact area at that load, Er is the Young’s modulus, and β is the correction factor that depends on the geometry of the indenter (for the Berkovich
tip, β is 1.034).

Also, we determined the elastic recovery (hmax − hf) for nanostructured transparent MgAl2O4 ceramics indented at different applied loads. The results showed that there was a
higher degree of plastic deformation at a higher applied load, as shown in the inset
of Figure 1.

The load-depth curve (Figure 1) is characterized by a substantial continuity, i.e., there are no large steps (pop-ins
or pop-outs) observed in both loading and unloading. Figure 1 shows high elastic recovery (70.58%) and low plastic deformation (29.42%). However,
when different loads were applied from 300 to 9,000 μN, it was observed that there
was an appreciable increase in plastic deformation. In fact, from the present calculation
of the depth before and after removal of the applied load, it was found that 57.72%
of the total work done during the indentation is attributed to elastic deformation.

Images of the nanoindentation were captured by the SPM mode, as shown in Figure 2A, which confirms the absence of any cracks and fractures around the indented zone.
Instead, the flow of the material along the edges of indent impressions can be clearly
seen. This flow is substantiated via a line trace of SPM images along the diagonal
section of the selected indent (bluish grey line in Figure 2A). The corresponding cross-sectional profiles are displayed in Figure 2B. Similar pile-ups around the indentation were observed in the nanocrystallization
during the nanoindentation of a bulk amorphous metal alloy at room temperature, indicating
the severity of plastic flow around this region during indentation [18]. Moreover, polycrystalline hydroxyapatite is reported to exhibit plasticity at higher
temperature [19,20], but no plasticity has been reported at room temperature for nanostructured transparent
ceramics. Furthermore, for ceramic materials, the plasticity is limited at low loads,
and the influence of dislocation can be important [21,22]. Thus, the faceted pile-up region suggests that dislocations generated during the
indentation are attributed to the residual strain of nanostructured transparent ceramics.

Figure 2.SPM image and corresponding cross-sectional profile. SPM image of an indented area (A) and the corresponding cross-sectional profile (B) along the bluish grey line in (A).

In order to further investigate the mechanical properties of nanostructured transparent
ceramics, we used HRTEM to examine the microstructures of the sample indented at 9,000
μN. The HRTEM image is shown in Figure 3. The inset in this figure is a selected area electron diffraction pattern of the
indented sample, indicative of a magnesia-alumina spinel crystal structure. The left
part of the HRTEM image reveals well-ordered atomic structures. However, there are
dislocations close to the triangular grain boundary, suggesting that the generation,
movement, and interaction of dislocations during the indentation play an important
role in the plastic deformation as well as the resulting mechanical properties.

Hardness and Young’s modulus of the nanostructured transparent MgAl2O4 ceramics are shown in Figure 4 as a function of the applied load. Both hardness and Young’s modulus decrease with
increasing loads. Furthermore, it also indicates that there appears to be a larger
decrease in the hardness than in the Young’s modulus with increasing load. These phenomena
have been attributed to the well-known indentation size effect. Gong et al. [14] studied an alumina ceramic by nanoindentation testing and found that more cracks
were generated at higher loads. However, the absence of cracks in the vicinity of
the indented zone (Figure 2) suggests that it should not be reasonable to explain the load-dependent mechanical
properties of our nanostructured transparent ceramics only by the indentation size
effect. Dislocation activity, as evidenced in Figure 3, compared to HRTEM images of the sample at atmospheric pressure [11] should be considered as an important factor that can influence the mechanical properties
of nanostructured transparent ceramics. A more detailed study is clearly needed to
understand how the dislocation activity influences the mechanical properties.

Figure 4.Hardness (A) and Young’s modulus (B) as a function of applied load. Inset shows TEM image of the sample.

It has been observed that the hardness and modulus of ceramic materials with a smaller
grain size have stronger load dependence than those with a larger grain size [23]. However, Young’s modulus is independent of the applied load when the load is above
10 mN [21]. Moreover, the contact depths in nanostructured samples indented at the lowest peak
loads are already equal to or larger than the average grain size, and thus, Young’s
modulus does not show any variation with increasing applied load [24]. In order to compare the hardness and modulus of our nanostructured transparent ceramics
with those of conventional large-grained ceramics, we averaged the hardness and modulus
data shown in Figure 4. The average hardness and modulus are 31.7 and 314 GPa, respectively. Our average
hardness is approximately twice that of large-grained (100 to 200 μm) MgAl2O4[25]. This is understandable since the well-known Hall–Petch relationship predicts that
a material with a smaller grain size should be harder than the same material with
a larger grain size. Both the average modulus (314 GPa) and the modulus (265 GPa)
measured at the maximum load (9,000 μN) are comparable to the Young’s modulus (277
GPa) of large-grained (100 to 200 μm) MgAl2O4[25]. This is also reasonable since it has been predicted that [26] the difference in Young’s modulus between porosity-free nanostructured materials
with a grain size larger than 10 nm and conventional large-grained materials should
be within approximately 5%.

Conclusion

In summary, the deformation behavior and the mechanical properties (hardness and Young’s
modulus) of the nanostructured transparent MgAl2O4 ceramics have been determined by nanoindentation tests. The degree of plastic deformation
increases with increasing applied loads. After the indentation test, scanning probe
microscope image shows no cracking, whereas high-resolution TEM image shows the evidence
of dislocation activity in nanostructured transparent MgAl2O4 ceramics. The measured hardness is much higher than that of conventional large-grained
MgAl2O4 ceramics, which should be of considerable interest to the fields of materials science
and condensed matter.

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

JZ carried out the sample preparation, analyzed SPM, and participated on the nanoindentation
analysis and paper corrections. TL analyzed the microstructures, evaluated the hardness
and modulus, and designed the study. XC analyzed the TEM and HRTEM. NW and JQ participated
in the study coordination and paper correction. All authors read and approved the
final manuscript.

Acknowledgments

This work was supported by the National Natural Science Foundation (NSFC) of the People’s
Republic of China under grant no. 50272040, Fok Ying Tong Education Foundation under
grant no. 91046, Youth Foundation of Science and Technology of Sichuan Province under
grant no. 03ZQ026-03, NSFC of the People’s Republic of China under grant no. 50742046,
NSFC of the People’s Republic of China under grant no. 50872083, and Doctor Foundation
of Ludong University under grant no. LY2012019. We thank T.D. Shen for his technical
assistance in preparing our manuscript.